Can I alter the biome of an area?

When Minecraft 1.2 is released, using the new “Anvil” file format, biomes will be stored in the chunk data so that they can be redefined on a per-column (x,z) basis. You will need an editor which supports doing so, or a generic NBT editor, of course. (Source)

This answer is now obsolete, please see Kevin Reid's answer for current information.

According to this, biomes are dependent on the level seed stored in the world. So, it means that, for every chunks, biomes are not saved in the chunk, but regenerated each time. You only chance a changing a biome would be to change the seed, but it would change every biome on the map, and new chunks won't match the old ones.